CSSE463: Image Recognition Day 15 Today: Today: Your feedback: Your feedback: Projects/labs reinforce theory; interesting examples, topics, presentation; favorite class; enjoying Projects/labs reinforce theory; interesting examples, topics, presentation; favorite class; enjoying Lecture and assignments OK or slightly too fast. Lecture and assignments OK or slightly too fast. Project intro Project intro Wrap up SVM and do demo, start lab 5 on your own Wrap up SVM and do demo, start lab 5 on your own Tuesday: Neural nets Tuesday: Neural nets Thursday: lightning talks (see other slides now), Lab 5 due Thursday: lightning talks (see other slides now), Lab 5 due Friday: lab for sunset detector Friday: lab for sunset detector 7 th week: Mid-term exam 7 th week: Mid-term exam

Review: SVMs: “Best” decision boundary The “best” hyperplane is the one that maximizes the margin, , between the classes. Equivalent to: The “best” hyperplane is the one that maximizes the margin, , between the classes. Equivalent to: Solve using quadratic programming Solve using quadratic programming margin 

Non-separable data Allow data points to be misclassifed Allow data points to be misclassifed But assign a cost to each misclassified point. But assign a cost to each misclassified point. The cost is bounded by the parameter C (which you can set) The cost is bounded by the parameter C (which you can set) You can set different bounds for each class. Why? You can set different bounds for each class. Why? Can weigh false positives and false negatives differently

Can we do better? Cover’s Theorem from information theory says that we can map nonseparable data in the input space to a feature space where the data is separable, with high probability, if: Cover’s Theorem from information theory says that we can map nonseparable data in the input space to a feature space where the data is separable, with high probability, if: The mapping is nonlinear The mapping is nonlinear The feature space has a higher dimension The feature space has a higher dimension The mapping is called a kernel function. The mapping is called a kernel function. Replace every instance of x i x j in derivation with K(x i x j ) Replace every instance of x i x j in derivation with K(x i x j ) Lots of math would follow here to show it works Lots of math would follow here to show it works Example: Example: separate x 1 XOR x 2 by adding a dimension x 3 = x 1 x 2 separate x 1 XOR x 2 by adding a dimension x 3 = x 1 x 2

Most common kernel functions Polynomial Polynomial Gaussian Radial-basis function (RBF) Gaussian Radial-basis function (RBF) Two-layer perceptron Two-layer perceptron You choose p, , or  i You choose p, , or  i My experience with real data: use Gaussian RBF! My experience with real data: use Gaussian RBF! EasyDifficulty of problemHard p=1, p=2, higher pRBF Q5

Demo Software courtesy of (GNU public license) Software courtesy of (GNU public license) Lab 5 (start today!): Lab 5 (start today!): Download the Matlab functions that train and apply the SVM. Download the Matlab functions that train and apply the SVM. The demo script contains examples of how to call the system The demo script contains examples of how to call the system Write a similar script to classify data in another toy problem Write a similar script to classify data in another toy problem Directly applicable to sunset detector Directly applicable to sunset detector Q1-2

Kernel functions Note that a hyperplane (which by definition is linear) in the feature space = a nonlinear boundary in the input space Note that a hyperplane (which by definition is linear) in the feature space = a nonlinear boundary in the input space Recall the RBFs Recall the RBFs Note how choice of  affects the classifier Note how choice of  affects the classifier

Comparison with neural nets Expensive Expensive Training can take a long time with large data sets. Consider that you’ll want to experiment with parameters… Training can take a long time with large data sets. Consider that you’ll want to experiment with parameters… But the classification runtime and space are O(sd), where s is the number of support vectors, and d is the dimensionality of the feature vectors. But the classification runtime and space are O(sd), where s is the number of support vectors, and d is the dimensionality of the feature vectors. In the worst case, s = size of whole training set (like nearest neighbor) In the worst case, s = size of whole training set (like nearest neighbor) But no worse than implementing a neural net with s perceptrons in the hidden layer. But no worse than implementing a neural net with s perceptrons in the hidden layer. Empirically shown to have good generalizability even with relatively-small training sets and no domain knowledge. Empirically shown to have good generalizability even with relatively-small training sets and no domain knowledge. Q3

Speaking of neural nets: Back to a demo of matlabNeuralNetDemo.m Back to a demo of matlabNeuralNetDemo.m Project discussion? Project discussion?